Binodal Research Articles

Phase transitions and critical properties of 1-propanol–n-hexane system

By using experimental data on p, T, x and p, T, ρ, x - relations of 1-propanol- n-hexane mixtures (0.2, 0.5, 0.8 and 0.9 mol. fraction of n-hexane x) and the method of isochore fracture p = f (T)ρ,x at two-phase (liquid-gas), one-phase (liquid, gas), near-critical and supercritical region liquid ↔ gas (ps, ρs, Ts) phase transition parameters are determined. And parameters of critical points (pc, ρs, Tc) are determined by the grapho-analytical method combining with scaling behavior. The dependence of pressure from temperature, density and composition along the phase coexistence curve is described by three parameter polynomial represented by expansion of the compressibility factor Z = p/RTρ into a power series of density ω = ρ/ρk and temperature , and .The average relative deviation of calculated values of pressure from experimental ones is 1%. The dependence of temperature from density along the liquid ↔ gas phase coexistence curve is described by equations: far from critical points ρ = ρk (1 ± B0τβ0 + B1τβ1 ± B2τβ2 + …), and in the symmetrical part of equilibrium curve (ρf – ρg)/2ρk = B0τβ0 + B2τβ2 + B4τβ4 + …, where τ = (T – Tk )/Tk and ω = (ρ – ρk)/ρk. Average relative error is 1.47%.

Liquid–Liquid Equilibrium and Extraction Performance of Aqueous Biphasic Systems Composed of Water, Cholinium Carboxylate Ionic Liquids and K2CO3

Ionic-liquid-based aqueous biphasic systems (IL-based ABS) have been broadly investigated for the separation of high-value compounds. Nevertheless, the large-scale application of IL-based ABS is still hampered by the high cost and hazardous features of most ILs used. Aiming at characterizing novel ABS composed of ILs with a more acceptable environmental footprint and enhanced biocompatibility, in this work, ABS formed by water, cholinium carboxylate ILs ([Ch][CnCO2], with n = 2 to 6), and K2CO3 were investigated. The respective ternary phase diagrams, including binodal curves, tie-lines, and critical points, were determined at (298 ± 1) K and atmospheric pressure. The capability to form ABS (or of the IL to be salted-out) increased with the increase of the alkyl chain length of the IL anion up to cholinium pentanoate; however, for longer anion alkyl chain lengths the ILs self-aggregation led to a decrease of the ILs ability to form ABS. Furthermore, the liquid–liquid equilibrium data experimentally determ...

Separation of erythromycin using aqueous two-phase system based on acetonitrile and carbohydrates

In this work, the ability of aqueous two-phase system (ATPS) based on carbohydrates (sorbitol, maltose monohydrate, and fructose) and acetonitrile for separation of erythromycin was investigated. For this purpose, binodal curves and tie-lines for three ATPSs were determined. The LLE data was also successfully correlated with the Othmer-Tobias and the Bancroft equations. The effective excluded volume (EEV) model was used to estimate the soluting-out ability of carbohydrates. Moreover, the partitioning of erythromycin in the ATPS was studied. Furthermore, the effect of carbohydrate and acetonitrile concentrations as well as temperature on the partitioning behavior of erythromycin were examined. In order to estimate the effect of temperature on the partitioning of erythromycin, molar Gibbs energy (ΔGEA), molar entropy (ΔSEA), and molar enthalpy (ΔHEA) were calculated. In all ATPSs the top phase is acetonitrile-rich while the bottom phase is carbohydrate-rich and erythromycin tends to migrate to the top phase. The results show that sorbitol has a higher soluting-out ability than maltose monohydrate and fructose. In addition, it can be concluded that the partitioning process of erythromycin is exothermic and the partition coefficient was decreased with increasing of erythromycin content.

The role of ionic association of choline amino acid ionic liquids on the two-phase formation and extraction of bovine serum albumin in ATPSs containing PEGDME250 and choline histidine or choline arginine at different temperatures

The choline amino acid ionic liquids, [Ch][AA]-ILs, as atoxic task-specific solvents are used for inducing an aqueous two-phase systems, ATPSs, in the presence of polymers such as polyethylene glycol di-methyl ether 250, PEGDME250. In these ILs, depending on anions structure the varied and strong interactions are existed between choline cation, [Ch]+, and amino acid anions, [AA], leading to an increase of ion association. These interactions affect ILs hydration behavior and therefore the studying of these ionic associations in some detail are useful in regard to phase formation ability. In this respect, binodal curve locations and tie-lines for ATPSs composed of PEGDME250 and choline histidine or choline arginine have been determined at three temperatures (298.15–318.15) K under atmospheric pressure (≈85 kPa) and followed by searching the effects of structure and ionic association of ILs together with temperatures on the phase diagram. The ionic association constants of the above ILs together with the previously studied ILs were calculated from ionic conductivity measurements made on the these binary aqueous IL solutions at T = (288.15–318.15) K using low concentration Chemical Model method. For correlation of equilibrium data the Othmar-Tobias, Bancraft and Setschenow equations along with osmotic virial and NRTL (e-or m-NRTL) models were utilized. Finally, influences of ionic association of ILs and temperature were investigated on the separation of bovine serum albumin. The results show that phase forming ability of different [Ch][AA]-ILs is increased by decreasing of Ka values which is parallel with decreasing of amino acid hydrophobicity.

Interfacial free energy of a liquid-solid interface: Its change with curvature

We analyze the changes in the interfacial free energy between a spherical solid cluster and a fluid due to the change of the radius of the solid. Interfacial free energies from nucleation studies using the seeding technique for four different systems, being hard spheres, Lennard-Jones, and two models of water (mW and TIP4P/ICE), were plotted as a function of the inverse of the radius of the solid cluster. In all cases, the interfacial free energy was a linear function of the inverse of the radius of the solid cluster and this is consistent with Tolman's equation. This linear behavior is shown not only in isotherms but also along isobars. The effect of curvature on the interfacial free energy is more pronounced in water, followed by hard spheres, and smaller for Lennard-Jones particles. We show that it is possible to estimate nucleation rates of Lennard-Jones particles at different pressures by using information from simple NpT simulations and taking into account the variation of the interfacial free energy with the radius of the solid cluster. Neglecting the effects of the radius on the interfacial free energy (capillarity approximation) leads to incorrect values of the nucleation rate. For the Lennard-Jones system, the homogeneous nucleation curve is not parallel to the melting curve as was found for water in previous work. This is due to the increase in the interfacial free energy along the coexistence curve as the pressure increases. This work presents a simple and relatively straightforward way to approximately estimate nucleation rates.

Phase Equilibria and Mutual Diffusion in Liquid Lithium-Sodium Alloys

The shape of the liquid-liquid coexistence line in the phase diagram of a lithium-sodium system is determined using the gamma-ray attenuation technique. The measured coordinates of the critical point of the coexistence curve (critical temperature TC = 576.8 ± 1.0 K; critical composition XC= 35.9 ± 0.4 at. % Na) are in good agreement with the data in the literature. The critical exponent β for the coexistence curve is 0.34 ± 0.004 in the range 1 · 10−3 < (TC—T)/TC < 5 · 10−2. Mutual diffusion in a Li-=Na melt of near-critical composition is studied at temperatures of 583 to 998 K using the same technique. The behaviour of the interdiffusion coefficient is found not to obey the Arrhenius law at temperatures below 700 K. Darken’s relation is used to estimate the temperature dependence of the long-wave limit SCC(0) of the Bhatia-Thornton concentration-concentration correlation function.

Thermodynamic properties of the 3D Lennard-Jones/spline model

The Lennard-Jones (LJ) spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at . We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be and , respectively. The triple point is estimated to and . The coexistence densities, saturation pressure, and supercritical isotherms of the LJ spline model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that the mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

On the use of aqueous solutions of polyvinyl methyl ether for the embolization of blood vessels

Aqueous solutions of polyvinyl methyl ether were investigated in order to test whether it is possible to utilize them as bases for embolic agents used to deliberately block blood vessels. This may be necessary in the course of treatment of vascular abnormalities, tumors, as well as during the preparation of patients for surgery. The right branch of the binodal curve for the binary system “polyvinyl methyl ether–water” was drawn using the cloud point method and the lower critical mixing temperature (35.5 °C) was calculated. Furthermore, the exact concentration of polyvinyl methyl ether in aqueous solutions at which phase transition occurs (given the temperature of 35.5 °C) was found to be 30 wt %. The viscosity–velocity curves for the 30% solution of polyvinyl methyl ether, obtained by rheoviscometry in the temperature range of 5 to 36 °C, indicate that this aqueous solution has a low viscosity and behaves like a Newtonian fluid. However, at the temperature of 35 °C and higher, close to the phase transition, a significant deviation from its Newtonian behavior is observed due to precipitation of polyvinyl methyl ether as it forms a solid white mass. Through the use of the Arrhenius–Frenkel–Eyring equation, the activation energy of the viscous flow for polyvinyl methyl ether solutions was found to be 31 kJ/mol. Based on refractometry data, it was demonstrated that phase transition in aqueous solutions of polyvinyl methyl ether is reversible. This feature can facilitate medical equipment cleaning before introducing the embolic agent into a patient’s bloodstream. Finally, the investigation determined some parameters, in which the formation of embolic agents from a 30% polyvinyl methyl ether aqueous solution occurs (in situ in a blood vessel at a temperature of 35.5 °C).

Liquid-liquid equilibrium of acetic acid – ethanol – ethyl acetate – water quaternary system: Data review and new results at 323.15 K and 333.15 K

A brief review of data on solubility and liquid-liquid equilibrium (LLE) in the acetic acid – ethanol – ethyl acetate – water system is presented. A new set of experimental data on solubility, LLE, and critical phases in this quaternary system, ternary subsystems (acetic acid – ethyl acetate – water, ethanol – ethyl acetate – water) and binary subsystem ethyl acetate – water are presented for 323.15 K and 333.15 K at atmospheric pressure. The gas chromatography and the cloud point technique were used to obtain experimental data. Binodal curves, surfaces, and critical manifolds are presented including 3D phase diagrams in composition tetrahedron. Experimental LLE data were correlated using the NRTL model.

Phase behavior for 1-butyl-3-methylimidazolium tetrafluoroborate with sodium oxalate/succinate/formate aqueous two-phase systems at 298.15 and 308.15 K

The liquid––liquid equilibrium (LLE) data and phase composition of the aqueous 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim]BF4) + sodium oxalate (Na2C2O4), [Bmim]BF4 + sodium succinate (Na2C4H4O4) and [Bmim]BF4 + sodium formate (NaHCOO) mixtures have been measured at 298.15 and 308.15 K. The effect of salts and temperature on binodal curves were studied in this work and a significant relationship has been observed between the salting-out ability and the Gibbs energy of hydration of the ions. The binodal data obtained were correlated by the Pirdashti and Merchuk equations and the tie-line compositions were well-fitted by the Othmer-Tobias and Bancroft equations and the experimental tie-line data were well correlated with extended UNIQUAC model. Additionally, the effective excluded volume values were also determined to analyze the salting-out abilities of the three salts which follow the order of Na2C2O4 > Na2C4H4O4 > NaHCOO.

Mono- and di- cationic ionic liquids based aqueous biphasic systems for the extraction of diclofenac sodium

The water and soil pollution by pharmaceutical residues is considered one of the major environmental concerns. Most conventional methods adopted for the removal of pharmaceutical wastes are associated with high consumption of energy, time and use of volatile organic solvents. With the focus to propose economically viable and environmentally benign extraction systems, liquid-liquid extraction (LLE) approach was used to remove pharmaceutical pollutants. Aqueous biphasic systems (ABS) that are a category of LLE proved to be competent techniques for extraction of compounds of pharmaceutical interest. In this context, we proposed ABS based on monocationic and dicationic ionic liquids (MILs and DILs) and scrutinized for their ability to extract model non-steroidal anti-inflammatory drug i.e., diclofenac sodium. To date, active research has been carried out on ABS formed by MILs and the DILs ability to form phases remains unexplored. In this work, we synthesized imidazolium, pyrrolidinium, morpholinium and ammonium-based MILs and corresponding DILs with bromide as common anion. The ability of synthesized ILs to undergo phase separation was explored in combination with various potassium salts such as K3PO4, K2HPO4 and K2CO3 at 298.15 K and atmospheric pressure. The phase behavior of proposed ABS was analyzed with the aid of phase diagrams, binodal curves and tie-lines of selected ternary systems composed of ILs, potassium salts and water. The systematic comparison of phase formation by MILs and DILs has been carried out. Further, the extraction capability of the designed ABS was evaluated for diclofenac sodium by using UV–visible spectroscopy. The proposed MILs and DIL based ABS showed appreciable ability to undergo phase formation as well as to extract the pharmaceutical compound of interest.

Understanding the role of the hydrogen bond donor of the deep eutectic solvents in the formation of the aqueous biphasic systems

Deep eutectic solvents (DES) have been proposed as phase-forming compounds of aqueous biphasic systems (ABS). However, due to DES nature and the high water content of the ABS, their nature and behavior remains controversial. To foster the understanding of DES-based ABS, the present work uses the relative hydrophilicity of the hydrogen bond donor (HBD) as a descriptor to clarify its role on ABS formation and phase properties. Dipotassium phosphate (K2HPO4)-based ABS phase diagrams composed of cholinium chloride ([N111(2OH)]Cl), as hydrogen bond acceptor (HBA), and several HBD (alcohols and sugars) were compared in molality units and the saturation solubility point for each binodal curve determined. The results here reported establish the HBD role as function of its relative hydrophilicity: very hydrophilic HBD act only as an adjuvant in the formation of ABS; HBD of intermediate hydrophilicity influence the ABS formation; while the most hydrophobic HBD tend to form organic-aqueous two-phase systems, where the HBA acts as an adjuvant to the system.

Phase Diagrams of n-Type Low Bandgap Naphthalenediimide-Bithiophene Copolymer Solutions and Blends.

Phase diagrams of n-type low bandgap poly{(N,N′-bis(2-octyldodecyl)naphthalene -1,4,5,8-bis(dicarboximide)-2,6-diyl)-alt-5,5′,-(2,2′-bithiophene)} (P(NDI2OD-T2)) solutions and blends were constructed. To this end, we employed the Flory–Huggins (FH) lattice theory for qualitatively understanding the phase behavior of P(NDI2OD-T2) solutions as a function of solvent, chlorobenzene, chloroform, and p-xylene. Herein, the polymer–solvent interaction parameter (χ) was obtained from a water contact angle measurement, leading to the solubility parameter. The phase behavior of these P(NDI2OD-T2) solutions showed both liquid–liquid (L–L) and liquid–solid (L–S) phase transitions. However, depending on the solvent, the relative position of the liquid–liquid phase equilibria (LLE) and solid–liquid phase equilibria (SLE) (i.e., two-phase co-existence curves) could be changed drastically, i.e., LLE > SLE, LLE ≈ SLE, and SLE > LLE. Finally, we studied the phase behavior of the polymer–polymer mixture composed of P(NDI2OD-T2) and regioregular poly(3-hexylthiophene-2,5-dyil) (r-reg P3HT), in which the melting transition curve was compared with the theory of melting point depression combined with the FH model. The FH theory describes excellently the melting temperature of the r-reg P3HT/P(NDI2OD-T2) mixture when the entropic contribution to the polymer–polymer interaction parameter (χ = 116.8 K/T − 0.185, dimensionless) was properly accounted for, indicating an increase of entropy by forming a new contact between two different polymer segments. Understanding the phase behavior of the polymer solutions and blends affecting morphologies plays an integral role towards developing polymer optoelectronic devices.

Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

Multi-spinning higher dimensional Kerr-AdS black holes admit the stable small-large black hole phase transition of van der Waals type. In this paper, we study the exact critical phenomena and phase structure in five-dimensional spacetime. First, we examine the thermodynamic laws in the reduced parameter space and find that they are quite different from the conventional thermodynamic laws. Then based on the reduced laws, the phase structure in different parameter spaces is investigated. The stable and metastable black hole phases are clearly displayed. We present a highly accurate fitting formula for the coexistence curve of small and large black hole phases. Using this fitting formula, we examine the critical exponents when the black hole system approaches the critical point along the coexistence curve. Moreover, employing the dimensional analysis and symmetry analysis, we also give a numerical study of the critical point for the unequal spinning black holes. These results are very useful on further understanding the microstructure of the multi-spinning black holes in higher dimensional spacetime.

R -crossing method applied to fluids interacting through variable range potentials

The R-crossing method of thermodynamic geometry is applied to reproduce the coexistence curves of fluid systems described by hard-core Yukawa and hard-core Mye-Type interactions whose range can be varied. Connection between the range of the potential and the validity of the method is studied. Even when scaling relations suggest a dependence on the range, we found explicitly the quantitative dependence for two varying range potentials. Using the saturation pressures, it is possible to assign a percentage P(λ) of measuring how far we can go below the critical point when reproducing the coexistence curve. It is found that there is a close relation between the range of the potential and P(λ). Such relation assures that the larger the range of the potential, the deeper we can go below the critical point. Our results, together with the known low |R| limit, represent two independent criteria to restrict the applicability of the R-crossing method. Namely, at what extent we can accurately reproduce the coexistence curve when we know the range of the intermolecular potential of the thermodynamic system involved.

A continuum framework for modeling liquid-vapor interfaces out of local thermal equilibrium

Continuum numerical methods modeling liquid-vapor phase change processes typically assume local thermal equilibrium at the liquid-vapor interface – continuity of temperature at phase interfaces, and a relation between interfacial saturation pressure and temperature based on phase co-existence curves. Several standard macroscopic problems have been solved accurately by adhering to this assumption. However, in micro-scale and certain non-standard macro-scale applications, significant jumps in temperature are observed at liquid-vapor interfaces during phase change, and vapor pressure can be far from equilibrium values. In this paper, we present a locally discontinuous arbitrary Lagrangian Eulerian finite element formulation with temperature discontinuities at interfaces. A penalty-based approach is used to weakly enforce the temperature jump condition. Furthermore, we use kinetic-theory-based Schrage relationship to evaluate the rate of phase change. We apply our methodology to solve the problem of flowing vapor in a planar heat pipe. The flow rates predicted by our continuum simulations are in excellent agreement with recently published molecular dynamics simulation results of the same problem. Interestingly, accounting for temperature discontinuities leads to only a slight improvement in the prediction of mass fluxes as compared to the case when temperature continuity is assumed. This is in contrast to the large improvement in the prediction of temperature profiles and is a consequence of a weak dependence of the evaporation/condensation rates on the vapor temperature.

Non-ionic surfactants and ionic liquids are a suitable combination for aqueous two-phase systems

The aqueous two-phase systems composed of the non-ionic surfactant Tergitol NP10 and the ionic liquids 1-ethyl-3-methyl imidazolium methylsulfate or 1-ethyl-3-methyl imidazolium ethylsulfate (C2C1imC1SO4 or C2C1imC2SO4) were characterized by the cloud point method. First, the binodal curves were determined and compared with the data reported previously for other non-ionic surfactants belonging to Tween and Triton families, observing that the systems belong to Treybal type 0 classification. Then, the experimental data were discussed in the light of the hydrophobicity of the surfactants and ionic liquids. The effect of the operation temperature (298.15, 313.15, 323.15, 333.15 K) was also evaluated at atmospheric pressure.

Cold Crystallization Temperature Correlated Phase Separation, Performance, and Stability of Polymer Solar Cells

Summary Fabrication of non-fullerene (NF)-based polymer solar cells (PSCs) has been an arduous task involving various approaches to optimize the morphology of blend film for superior performance. In this work, unique exothermic peaks can be observed in differential scanning calorimetry first heating scan of the blend films, which are assigned to the cold crystallization temperature (TCC) of NF acceptors when blended with different degree of crystallinity polymers, and TCC contains the phase information at quenched stage of the film development. A linear correlation between the phase separation parameters and TCC was established, which helps to select the appropriate donor for a specific acceptor. Utilizing multiple polymer-NF blend systems, we report an expectation TCC value between 210°C and 230°C, which would promise balanced domain size, purity, and consequentially superior performance. Further investigation revealed that TCC can also be used to evaluate the thermal stability.

Molecular theory of a ferromagnetic nematic liquid crystal.

We employ a version of classical density functional theory to study the phase behavior of a simple model liquid crystal in an external field. The uniaxially symmetric molecules have a spherically symmetric core with superimposed orientation-dependent attractions. The interaction between the cores consists of a hard-sphere repulsion plus an isotropic square-well attraction. The anisotropic part of the interaction potential allows for the formation of a uniaxially symmetric nematic phase. The orientation of the molecules couples to an external polar field. The external field is capable of rotating the nematic director n[over ̂] in the x-z plane. The field is also capable of changing the topology of the phase diagram in that it suppresses the phase coexistence between an isotropic liquid and a nematic phase observed in the absence of the field. We study the transition from an unpolar to a polar nematic phase in terms of the orientation-distribution function (odf), nematic and polar order parameters, and components of n[over ̂]. If represented suitably the odf allows us to study orientational changes during the switching process between nonpolar and polar nematic phases. We also give a simple argument that explains why nematic order is lost whereas polar order persists up to the gas-liquid critical point along the coexistence curve. We also discuss the relevance of our theory for future experimental studies.

On the liquid–vapour coexistence curve in a Lennard–Jones fluid

A hard-core double Yukawa potential is taken as an approximation of the Lennard–Jones (LJ) potential. Using first-order thermodynamic perturbation theory with a hard-sphere fluid as the reference system, the equation of state of the hard-core double Yukawa fluid is derived analytically. Adjusting the hard-core diameter with the Barker and Henderson prescription to account for the repulsive part of the LJ potential, the liquid–vapour coexistence curve of the LJ fluid is computed with such equation of state. The results are compared with simulation data for the LJ fluid and very good agreement is observed.